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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="FFEToElt"></a>
FFEToElt
</h2>

Returns a canonical representative of a finite field element viewed
as a representative of a class of algebraic numbers.

<p><p>

<h3>
Syntax:
</h3>
<pre>a := FFEToElt( f, p);</pre>

<p>

<table>
<tr>
<td>finite field element</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  p  </pre></td>
<td>must be prime</td>
</tr>
<tr>
<td>algebraic number or integer</td>
<td><pre>  a  </pre></td>
<td>interpreted as algebraic number</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#IdealResidueField">IdealResidueField</a>, <a href="kashref.html#IdealResidueFieldIsomorphism">IdealResidueFieldIsomorphism</a>, <a href="kashref.html#EltToFFE">EltToFFE</a>

<p>

<h3>
Description:
</h3>
This is a inverse function of EltToFFE, and a embedding
O / {\goth{p}} rightarrow O. 
The prime ideal must not lie over a number which divides the degree
of the order.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> O := OrderMaximal(Order(Poly(Zx,[1,4,1,-4,-3,7])));
Generating polynomial: x^5 + 4*x^4 + x^3 - 4*x^2 - 3*x + 7
Discriminant: 28442269 

kash> p := Factor(7*O)[1][1];
<7, [0, 1, 0, 0, 0]>
kash> b := Elt(O,[3, 1,5,1,8]);
[3, 1, 5, 1, 8]
kash> n := EltToFFE(b, p);
3
kash> FFEToElt(n, p);
> 3

</pre>

<p>


<hr>

<p>
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